MODEL ANSWERS FOR PREDTRAN
Note: put a blank on either side of ‘v’ when it is used to mean “or”, rather than a variable.
Problem Set 1
(1) Lac : Alfred loves Claudia
(2) Laa : Alfred loves himself
(3) (x)(Dx > Ux) : All dogs are ugly
(4) (Ex)(Dx & Ux) : Some dogs are ugly
(5) (Ex)Lax : Alfred loves something
(6) (x)Lxa : Everything loves Alfred
(7) (Ex)Lxx : Something loves itself
(8) (x)~Lxx : Nothing loves itself
(9) (Ex)((Dx & Ux) & ~Cx) : Some ugly dogs are not cats
(10) ((Ex)(Dx & Nx) & (Ey)(Cy & ~Ny)) : Some dogs run and some cats don't
(11) (x)((Sx & Cx) > ~(Ox & Dx)) : No strange cat is a nosey dog
(12) (Ex)(Dx & (Ox & Ux)) : Some dogs are nosey and ugly
(13) (x)((Dx v Cx)>(Ox & Ux)) : All dogs and cats are nosey and ugly
(14) (x)(Gx > Lxa) : Every logician loves Alfred
(15) (x)(Gx > Rdx) : Every logician is resented by Dagmar
(16) (Ex)(Lxc & Rxe) : Something loves Claudia and resents Eva
(17) ((Ex)Lxc & (Ey)Rye) : Something loves Claudia and something resents Eva
(18) (x)((Ux & Gx) > ~Ldx) : No ugly logicians are loved by Dagmar
(19) (x)(Gx > Rxb) > Rab : If every logician resents Bart then so does Alfred
(20) (Ex)(Gx & ((y)(Dy > Rxy) & (Ez)(Cz & Lxz))) : Some logician who resents all dogs loves some cat
Problem Set 2
(1) Ocn : California overlaps North America
(2) Pnc : North America is part of California
(3) ~Odc : Delaware doesn't overlap California
(4) (x)(Oxs > Oxc) : Whatever overlaps San Diego overlaps California
(5) (x)(y)(Pxy > Oxy) : Every part of a thing overlaps that thing
(6) (Onc & ~Pnc) : North America overlaps California, but is not part of it
(7) (x)(Pxc > ~Pxd) : No part of California is part of Delaware
(8) (x)(Ey)(Oxy & ~Pxy) : Everything overlaps something it isn't part of
(9) (Ex)(Pxo & ~Pxc) : Some part of the Universe is not part of California
(10) (Pcn ≡ (x)(Oxc > Oxn)) : California is part of North America if and only everything that overlaps California overlaps North America
(11) (x)(Pxo > (Ey)(Gy & Hyx)) : Every part of the Universe is hated by some logician
(12) (x)(y)(Oxy > Oyx) : Everything that overlaps a thing is overlapped by that thing
(13) (x)((~Oxx v ~Pxx) > Tx) : Everything that doesn't overlap itself or is not part of itself is abstract
(14) (x)((Gx&Oxc) > Nx) : Every logician who overlaps California runs
(15) (x)((Ey)(Pyo & Pxy) > Pxo) : Every part of a part of the Universe is a part of the Universe
(16) (x)((Tx & Gx) > (y)(Hyc > Hyx)) : All abstract logician are hated by all who hate California
(17) (x)(((Gx & Hxs) & ~Hxc) > ~Hxd) : Logicians who hate San Diego but not California don't hate Delaware either
(18) (x)((Ey)((Ty & Gy) & Hxy) > (Ez)((Nz & Gz) & Hxz)) : Anything which hates an abstract logician hates a logician who runs
(19) (x)(Tx > ~(Ey)(Pxy & Gy)) : Nothing abstract is part of any logician
(20) (x)((Pxn & ~(Oxd v Oxc)) > ~(Ey)(Gy & Oxy)) : No part of North America that overlaps neither Delaware nor California overlaps any logicians BUG: The computer may not accept the right answer on this one